| Topic | People | Description | |
|---|---|---|---|
| Calculus of variations and optimal control; optimization standard compliant MSC | |||
| Optimality conditions |
Sisto Baldo |
Asymptotics of variational problems. Variational convergences and Gamma Convergence. Singular perturbations of variational problems. | |
| Variational principles of physics |
Sisto Baldo Giacomo Canevari Giandomenico Orlandi |
Variational problems from condensed matter and particle Physics (e.g. Ginzburg-Landau models for superconductivity, Gross-Pitaevskii model for Bose-Einstein condensation, string theory, Landau-de Gennes model for liquid crystals) and their relation with minimal surfaces. | |
| Existence theories |
Sisto Baldo |
Minimal surfaces. Calculus of variations on manifolds. | |
| Hamilton-Jacobi theories, including dynamic programming |
Antonio Marigonda |
Nonsmooth Analysis and application to Optmal control. Viscosity solutions of Hamilton-Jacobi equations. | |
| Manifolds standard compliant MSC | |||
| Variational problems in a geometric measure-theoretic setting |
Sisto Baldo Mauro Bonafini Giacomo Canevari Antonio Marigonda Giandomenico Orlandi |
Geometric variational and evolution problems: minimal surfaces, motion by mean curvature. Optimal mass transport theory. | |
| Geometric measure and integration theory, integral and normal currents in optimization |
Giandomenico Orlandi |
Geometric measure theory, integral and normal currents; optimization problems for networks of curves and surfaces. | |
| Optimal Transport |
Mauro Bonafini Antonio Marigonda Giandomenico Orlandi |
Analytical and geometrical methods for the study of problems of optimal mass transportation and optimal resource allocation. | |
| Numerical analysis standard compliant MSC | |||
| Exponential integrators and approximation of matrix functions |
Marco Caliari |
Analysis and implementation of exponential integrators for stiff equations by efficiently approximating matrix functions of exponential type, with application to systems of diffusion-reaction equations (Turing pattern), nonlinear Schrödinger equations, and Ginzburg-Landau equations (soliton and vortex dynamics). | |
| Numerical methods and models for multi-scale systems of interacting particles |
Giacomo Albi |
Analysis and implementation of mathematical methods and models for dynamics of systems of interacting particles on various scales and their control: data-driven control for high-dimensional systems with non-local interaction; particle methods for problems of global optimization and applications to machine learning; dynamics of opinions on social networks; multi-scale models for crowd dynamics, and optimal strategies for evacuation problems; socio-epidemiological models and strategies to mitigate the spread of infection; control problems for high energy particles for the confinement in plasmas, and for targeted radiotherapy in treatment of tumors. | |
| Numerical solution of partial differential equations |
Giacomo Albi Marco Caliari Elena Gaburro |
Analysis and implementation of innovative and effective numerical methods for solving and controlling partial differential equations (PDEs) of parabolic type (diffusion-transport-reaction), hyperbolic type (e.g. Euler equations for gas dynamics and Einstein field equations for astrophysics), highly oscillatory (Schrödinger equations), and integro-differential equations (kinetic equations with term collision and mean-field equations with non-local interaction terms). | |
| Development of novel Finite Volumes and Galerkin Discontinuous numerical methods with Structure Preserving properties |
Elena Gaburro |
Conception, analysis and HPC development of novel high-order accurate Finite Volumes (FV) and Discontinuous Galerkin (DG) numerical methods for the solution of hyperbolic equations. The equations of interest are: the Euler equations of gas-dynamics, Shallow Water equations for the field of fluid-dynamics, MHD and GRMHD for magnetohydrodynamics, Baer-Nunziato for multiphase, GPR for continuum mechanics and the Einstein field equations for general relativity. The methods developed are high-order accurate, structure preserving (i.e., preserving additional physical features as equilibria, involution constraints and asymptotic limits) and Arbitrary-Lagrangian-Eulerian (ALE). The algorithms are implemented on adaptive Cartesian grids and on grids of triangles/tetrahedra, polygons/polyhedra and Voronoi also moving in time (the mesh generation and optimization are also the subject of our research). | |
| Partial Differential Equations standard compliant MSC | |||
| PDEs in connection with biology, chemistry and other natural sciences |
Francesco Ferraresso |
Well-posedness of systems of semilinear and quasilinear parabolic equations modelling the diffusion and aggregation of Aβ-amyloids in the brain, including chemotactical terms of Keller-Segel type. | |
| Maxwell equations |
Francesco Ferraresso |
Analysis of the spectral properties and spectral approximation of the Maxwell system, even with tensor coefficients and in dispersive media, including metamaterials. | |
| Elliptic equations and elliptic systems |
Sisto Baldo Giandomenico Orlandi |
Studying existence, regularity, and qualitative properties of solutions to second-order elliptic equations and systems of equations, possibly by variational techniques | |
| Spectral theory and eigenvalue problems for partial differential equations |
Francesco Ferraresso |
Eigenvalue analysis of elliptic differential operators, possibly of high order. Dependence of the spectrum upon geometrical perturbations, including Hadamard formulae. | |
| Stochastic analysis standard compliant MSC | |||
| Stochastic partial differential equations and their applications |
Luca Di Persio |
The research about (SPDEs and their applications spans a wide range of topics. With respect to theoretical contributions, we focus on fundamental aspects such as existence, uniqueness of solutions, invariant measures, and asymptotic expansions, with equations driven by general Lévy-type noises. Concerning applications, we consider mathematical finance problems exploiting SPDEs' methods to address challenges like option pricing under stochastic volatility, counterparty risk evaluation, and optimal execution strategies, often employing FBSPDEs and jump-diffusion models. Moreover, we consider control and optimization applications in memory-dependent systems, mean-field games, and stochastic control to manage uncertainty through dynamic programming and energy shaping. We also use SPDE techniques for electricity price forecasting, wind energy modelling, and control in robotics and teleoperation, emphasizing stochastic passivity and developing an innovative stochastic approach to port-Hamiltonian systems. Interdisciplinary applications extend to biomedicine, network dynamics, and interacting particle systems, showcasing the versatility of these mathematical tools in addressing complex problems in heterogeneous fields. | |
| Problem solving in the context of artificial intelligence |
Luca Di Persio |
The research fields covered by the Artificial Intelligence (AI) and Machine Learning we are interested in span various applications across finance, energy, and control systems. In finance, hybrid neural networks and deep learning are applied to forecasting, risk management, and investment optimization, including stock price prediction and volatility analysis. Energy systems benefit from AI-driven models for load forecasting, electricity price prediction, and renewable energy management. Stochastic control methods, enhanced by neural networks, address optimization challenges in dynamic and uncertain environments. Advanced neural architectures, such as recurrent networks and multitask learning, improve time series forecasting and domain-specific predictions. Interdisciplinary applications include biomedical engineering, where AI aids in analysing nanofluids, and robotics, where neural networks support motion control under stochastic dynamics. These studies emphasize the integration of AI to solve complex, high-impact problems. | |
| Large scale interacting random systems |
Francesca Collet Paolo Dai Pra |
This research field focuses on the study of complex systems composed of a large number of components that interact with each other according to probabilistic rules. The main goal is to understand how microscopic interactions give rise to the emergence of highly ordered or highly organized macroscopic collective behaviors, which are not easily predictable from the behavior of individual units. In more detail, the topics addressed include scaling limits, phase transitions, fluctuations, relaxation times, and applications to biology and social sciences. | |
| Name | Description | URL |
|---|---|---|
| Analysis of PDE and Calculus of Variations | Il gruppo si occupa di attività di ricerca nel campo del calcolo delle variazioni, teoria geometrica della misura, teoria del controllo ottimo, teoria del trasporto ottimo, e applicazioni. | |
| Contemporary Applied Mathematics | Sviluppo di metodi matematici teorici e computazionali avanzati per fenomeni di trasporto e diffusione in sistemi complessi, l'approssimazione multivariata e problemi di controllo alto dimensionali. | |
| INdAM - Unità di Ricerca dell'Università di Verona | Raccogliamo qui le attività scientifiche dell'Unità di Ricerca dell'Istituto Nazionale di alta Matematica INdAM presso l'Università di Verona |
© 2025 | Verona University
******** CSS e script comuni siti DOL - frase 9957 ********
